Maximal volume of cup for a given area of material

Perfect Paper Cup Company (PPCC) wants to make a cylindrical cup (with
open top, of course, so people can drink out of it). The cup is to be made from
exactly 22 in2 of paper—not counting any paper wasted in cutting out the circular
bottom, in attaching the bottom to the cylindrical piece, or in fastening
together the ends of the rectangle that’s rolled up to make the cylindrical
piece.